[en] It is known that D_p-brane effective action at the leading order of ${\alpha }^{\prime }$ in flat space–time which is given by DBI action, transforms to D${}_{p-1}$-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order ${\alpha }^{\prime }$, one may find corrections to the DBI action which include the second fundamental form Ω and the covariant derivative of gauge field strength DF, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of $DFDF$ and ΩΩ with zero, two, four and six F's. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature.